Short answer is no, long answer is maybe.
The Camry has a smaller hub diameter of 60.1, which means that if you have hub-centric wheels, then the wheels won't fit over the hub on the Civic. If you have Lug-centric wheels (generic), then yes, the wheels will fit.
There is also the issue that the Camry tires are wider and taller than those of the Civic. The Camry tires will have a diameter of 26.1", while the Civic tires have a diameter of 24.9". Therefore, the Camry tires will be 1" taller, and about .4" wider.
It's possible the extra inch of height won't cause any problems (rubbing), but its also possible that it will.